SPL function of speed or acceleration
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 26th May 2004, 01:50 PM #1 gary f   diyAudio Member     Join Date: Aug 2003 Location: Quebec city SPL function of speed or acceleration Hello Mathematicians out there. Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone. F
 26th May 2004, 02:38 PM #2 DanWiggins   diyAudio Member   Join Date: Aug 2002 Location: Seattle or Shanghai Acceleration of the cone. This is why the velocity doubles as you drop an octave, and the displacement quadruples as you drop an octave (assuming the SPL level stays the same). Dan Wiggins Adire Audio
gary f
diyAudio Member

Join Date: Aug 2003
Location: Quebec city
Thanks Dan,

I wonder, I saw the parthenon driver used as a dipole driver. How come the front pressure wave and rear pressure wave don't cancel each other?

F
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 26th May 2004, 06:19 PM #4 454Casull   diyAudio Member   Join Date: Jan 2004 Location: Toronto, ON, Canada They do if the Parthenon isn't put into an enclosure.
Svante
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Re: SPL function of speed or acceleration

Quote:
 Originally posted by gary f Hello Mathematicians out there. Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone. F

If mounted in a box it is proportional to the acceleration.

The pressure from a point source is:

p=(U*rho0*w)/(4*pi*r)

where U is the volume flow (m3/s), rho0 is the density of air (=1.2 m3/s), w is the angular frequency (rad/s), r is the distance. Free field conditions are assumed. For low frequencies, a loudspeaker can be approcimated by a point source, and volume flow U is:

U=Sd*v

where Sd is the equivalent piston area of the speaker, and v is the velocity of the cone.

So p is oproportional to w*v which in turn is equal to the acceleration (with a 90 degree phase shift).
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DanWiggins
diyAudio Member

Join Date: Aug 2002
Location: Seattle or Shanghai
Quote:
 Originally posted by gary f Thanks Dan, I wonder, I saw the parthenon driver used as a dipole driver. How come the front pressure wave and rear pressure wave don't cancel each other? F
They do cancel, as a dipole speaker should. With a baffle width of 24", it will start cancellation around 280 Hz, and roll off at 6 dB/octave below that. Of course, with so much displacement to start with, you can still do 110+ dB @ 20 Hz...

The concept was not only to make the wildest looking driver you've ever seen, but one with so much potential output that it's kind of a "so what" in terms of loss. There's so much to start with, you don't NEED a box.

Dan Wiggins

 26th May 2004, 09:32 PM #7 JMB   diyAudio Member   Join Date: Apr 2004 Location: Texas Based on your equations, it appears, then, that a more efficient or louder speaker of equal Sd would have a better transient response. Is this correct?
 27th May 2004, 03:32 AM #8 bhg41088   diyAudio Member   Join Date: Feb 2004 is there a video of that thing going at it? __________________ -
roddyama
diyAudio Moderator Emeritus

Join Date: Jan 2002
Location: Michigan
Re: SPL function of speed or acceleration

Quote:
 Originally posted by gary f Hello Mathematicians out there. Is Sound Pressure Level generated by a transducer proportional to speed of the cone or acceleration of the cone. F
OK, here we go.

Sound pressure is proportional to the cone velocity.

Two examples, one real and one conceptual.

1.) A jet plane has broken the sound barrier and is now traveling at a constant speed of mach 1.X. The "sonic boom" is a sonic pressure wave created by the plane traveling at a contasnt velocity. The planes acceleration is zero.

2.) A speaker cone is driven by a triangle wave signal and the cone follows the signal perfectly. The cone moves at a constant velocity and changes direction instantaneously at the ends of its travel. Sound pressure will be generated by the movement of the cone and the SPL will be proportional to the cones velocity. If the SPL were proportional to the acceleration, the SPL would be infinite.
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sreten
R.I.P.

Join Date: Nov 2003
Location: Brighton UK
Quote:
 Originally posted by JMB Based on your equations, it appears, then, that a more efficient or louder speaker of equal Sd would have a better transient response. Is this correct?
A very fallacious assumption.

A bit like amplifier slew rate requirements - which is faster :

a) a 10W 10V/us amplifier or
b) a 100W 20V/us amplifier ?

some would say b) by definition, but IMO its a).

sreten.

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